RL Circuits

RL Circuits have a combination of Resistors and Inductors as their name would suggest. What we need to do is combine the resistive elements of our circuit with the reactive ones. Due to the way inductors behave, you cannot just add the resistors and inductive reactance, but you can use the pythagorean theorem, and you can also use vector mapping and basic trigonometry functions.

Series RL

In a series circuit containing resistors and inductors, the current (I) is our reference vector.

Resistor voltage (Vr) is in phase, at 0 degrees. (Adj)
Inductive voltage (Vl) is at 90 degrees. (Opp)
and total voltage (Vt) is somewhere in between. (Hyp)
The phase angle (Theta) is the angle between R and Z and can be calculated by

Tan-1(Opp/Adj) or in this case Tan-1(Xl/R)

This is most common in electronic circuits. However, sometimes you might only have the impedance and the resistance, and need to find the inductive reactance.

Cos-1(Adj/Hyp) so Cos-1(R/Z)

We can use a 3/4/5 triangle to quickly show how this works. Let’s say we need to find impedance, and Xl = 4, R=3.